Lord Justice Thomas and Mr Justice Ouseley on Wednesday handed down their judgment in the 40-year-old Australian's appeal against a European arrest warrant issued by Swedish prosecutors after rape and sexual assault accusations made by two Swedish women following his visit to Stockholm in August 2010.

Assange, who was wearing a navy blue suit, pale blue tie and a Remembrance Day poppy, remains on bail pending a decision on a further appeal. The judges ruled the issuing of the warrant and subsequent proceedings were "proportionate" and dismissed arguments that the warrant had been invalid and descriptions of the alleged offences unfair and inaccurate.

Assange gave no sign of emotion as the judges gave reasons for the decision.

Assange's lawyers said they would take 14 days to decide whether to seek the right to appeal to the supreme court and said they would challenge the £19,000 costs against him, indicating he might not have the means to pay.

After the hearing, Assange made a short statement on the steps of the court, saying: "We will be considering our next step." He urged people to turn to a website set up in his support.

"No doubt there will be many attempts made to try to spin these proceedings as they occured today but they were merely technical. So please go to swedenversusassange.com if you wish to know what is really going on in this case."

Assange refused to answer shouted media questions as he left.

The judges rejected the appeal on all four grounds made by his legal team, opening up the possibility that Assange could be removed to Sweden by the end of the month.

Lord Justice Thomas said a date would be fixed in three weeks' time to hear any case by Assange that he should be allowed to take the case to the supreme court.

To appeal again, Assange must persuade the judges there is a wider issue of "public importance" at stake in the latest decision. If he is successful in persuading the high court of that, he is likely to remain on conditional bail until a hearing in front of the supreme court. This is unlikely to take place until next year.

If he is denied the right to appeal then British law enforcement officers will be responsible for arranging his removal to Sweden within 10 days.

Earlier Assange was surrounded by a melee of photographers as he arrived to hear the decision. Supporters had fixed banners to railings saying: "Free Assange! Free Manning! End the wars."

Bradley Manning is the detained American soldier alleged to have leaked hundreds of thousands of US diplomatic cables to WikiLeaks.

After the decision, supporters outside the court said they were outraged. Ciaron O'Reilly, 51, said: "Assange is probably the most amazing person in recent history who's upset so many powerful people in such a short space of time so it's obviously not a level playing field." The decision comes three and a half months after the end of an appeal hearing in July, when lawyers for Assange argued the arrest warrant was invalid because of significant discrepancies between its allegations of sexual assault and rape and the testimonies of the two women he allegedly had sex with.

Ben Emmerson QC, for Assange, had claimed the warrant "misstates the conduct and is, by that reason alone, an invalid warrant".

He recounted evidence of the encounter on the night of 13 August 2010 between Assange and a woman known as AA, who was hosting Assange at her apartment, during which AA said Assange tried to have sex with her without a condom.

Emmerson said there was no evidence of a lack of consent sufficient for the unlawful coercion allegation contained in the arrest warrant.

He argued the court had to decide only on whether the arrest warrant in connection with the events was valid on "strict and narrow" legal grounds.

Acting for the Swedish director of public prosecutions, Clare Montgomery QC said the charges detailed in the warrant were valid allegations and said AA, and another woman, known as SW, had described "circumstances in which they did not freely consent without coercion".

She said the definition of an extradition offence "means the conduct complained of. It has nothing to do with the evidence."

In February, when Assange challenged the extradition moves at Westminster magistrates court, his legal team warned their client could be at "real risk" of the death penalty of detention in Guantánamo Bay because they feared the US authorities would request his extradition from Sweden to face charges relating to WikiLeaks obtaining and publishing hundreds of thousands of classified US government documents.

The senior district judge threw out the appeal and ordered his extradition, and a week later Assange appealed to the high court.

He changed his legal team and adopted a less vocal strategy.

Assange has in effect been under house arrest at Ellingham Hall in Norfolk since December 2010. He has to sign in at a local police station every day, he wears an electronic tag that monitors his movements and he has to be back inside the house by 10pm each night.

Swedish prosecutors said Assange has been "detained in his absence on probable cause suspected of rape (less severe crime), sexual molestation and unlawful coercion."